Tammann1 has shown that in the hydrolysis of salicine by emulsin, the latter is gradually decomposed, and that the rate of decomposition of the ferment-i.e. the rate at which the ferment is rendered inactive-follows the course of a unimolecular reaction. Hence, as in § 12, it is easy to see that even after an infinite time some of the original substance must remain undecomposed, a conclusion which agrees with the work of Tammann.

Suppose, now, that the formation of the intermediate compound occupies a measurable time, the velocity of formation of the products of the action will be proportional to the amount of intermediate compound present in the solution at the time t The velocity of formation of M will be proportional to the amounts of A and of C present in the solution. Hence, with the same symbols as before, a-x-y denotes the amount of the original substance present at the time t, and c-y the amount of catalyzer present at the same time.

Hence

The velocity constant of a catalyzed reaction.--Let the velocity of a reaction be represented by the expression

where f'(C) is employed to represent the relation between the velocity and the concentration of the reacting substances, when we do not wish to commit ourselves to such a definite statement as is implied by the law of mass action, or when the disturbing influences are so great that we do not know what else to write on the left side of the above equation. By integration—

f(CC)= k(tt)....

(13)

1 G. Tammann, Zeit. phys. Chem., 16. 285, 1892; 18. 426, 1895.

If the reaction now takes place in the presence of a catalytic agent, and the value of k changes to k', while the form of the function f(C1- C2) remains the same, we have—

If we let the two reactions run on until the same amount of substance is transformed in each case, we get, from (13) and (14)—

That is to say, the intervals of time required for the transformation of the same amount of substance in a catalyzed and in a non-catalyzed reaction is inversely as the velocity constants of the two reactions.1

Hence it is possible to determine the change, «, effected by the catalytic agent upon the velocity constant of the normal reaction, even when the velocity equation is not known. We assume that the catalytic agent does not alter the actual form of f'(C). If the catalyzed reaction goes via an intermediate compound not formed with the simple reaction, (15) no longer holds good.

By a suitable transformation of the above equations, making k(t — t1) unity

This means that the increase which takes place in the velocity of a reaction in presence of a catalytic agent can be determined from the time required for the transformation of a certain amount of the substance in presence and in the absence of the catalytic agent.2

If the time t-t1 required for the transformation of the substance in the absence of the catalytic agent is very great in

1 W. Ostwald, Zeit. phys. Chem., 2. 134, 1888.

2 W. Ostwald, Zl.c.; T. S. Price, Zeit. phys. Chem., 27. 474, 1898; J. Brode, ib., 37. 257, 1901.

comparison with t-t, the second term of (16) vanishes, k is very small in comparison with k', and we get

This equation applies to the inversion of cane sugar, and it is only necessary to find how the constant k' changes with the quantity of the catalytic agent in different experiments.

As a rule, the acceleration is proportional to the amount of catalytic agent present. It is then possible to determine the amount of catalytic agent from the velocity of the reaction. Trevor and Palmaer1 have found that the rate of inversion of cane sugar is proportional to the concentration of the catalyzing acid, as the following numbers show :

:

Price also noticed that the catalytic action of ferrous sulphate in the reaction between potassium persulphate and potassium iodide is proportional to its concentration. If

denotes the velocity of the reaction in presence of the catalyst, then

gram

will be the velocity of the reaction in presence of molecules of the catalytic agent. The rule, however, is by no means general.

1

J. E. Trevor, Zeit. phys. Chem., 10. 330, 1892; W. Palmaer, ib., 22. 504, 1897; H. Goldschmidt with H. Larsen for the catalytic action of metallic chlorides in the chlorination of nitrobenzene-Zeit. phys. Chem., 48. 424, 1904; with K. Ingelbrechten, ib., 48. 435, 1904; T. S. Price, ib., 27. 474, 1898.

CHAPTER XII

INFLUENCE OF TEMPERATURE ON CHEMICAL

REACTIONS

§ 113. Influence of Temperature on Chemical Reactions. THE influence of temperature on chemical reactions is so very marked that this has been universally recognized as one of the most important factors in the study of chemical changes. Although many interesting facts have been brought to light by a happy combination of theory and experiment, this subject still forms, as Ostwald has said, one of the darkest chapters in chemical mechanics." The subject, too, is vested with a certain amount of technical interest, since the manufacturer must know the best temperature to keep unstable solutions, such as the "azo-colours" of the dye-house, in order to have a minimum loss by decomposition.1

66

The velocities of all chemical reactions, with few exceptions,2 increase rapidly with rise of temperature. For example, barium formate decomposes twice as rapidly at 330° as it

1 G. Bredig's Ueber die Chemie der extremen Temperaturen, Leipzig,

1901.

2 We have a few reactions in which the rate is diminished by raising the temperature. For example, the rate of liberation of iodine from a mixture of potassium iodide, ferrous sulphate, and chromic acid is less at 30° than at o° C. (C. C. Benson, Journ. Phys. Chem., 8. 116, 1904); the rate of reduction of ferric sulphate by iron in acid solution "appears to decrease with increase of temperature (T. E. Thorpe, Journ. Chem. Soc., 41. 287, 1882); and those reactions in which a colloidal catalyst is involved. Like negative catalyses, the explanation, when found, will turn on the presence of disturbing secondary reactions.

does at 260°;1 the inversion of cane sugar proceeds five times as fast at 55° as it does at 25°; 2 the conversion of solid ammonium cyanate into urea is fifty times as rapid at 57° as it is at 33;3 the transformation of dibromosuccinic acid into bromomaleïc acid goes three thousand times as rapidly at 101° as at 15°; and although the reaction between hydrogen and oxygen is so slow at 155° that no sign of combination can be detected after many months, yet, at about 600° the combination takes place with explosive violence.5 Dewar,

Alcohol transformed

4

FIG. 27.-Velocity curves.

too, has shown that at the temperature of liquid air (-183°) photographic action is 20 per cent., and at the temperature of liquid hydrogen (-250°), it is but Io per cent. of its value at ordinary temperatures. The rapid increase in the velocity of the esterification of alcohol as the temperature rises from 8° to 100° is shown graphically in

Fig. 27; the ordinates represent the amount of ethyl acetate transformed, the abscissæ the time. It must be particularly noticed that the abscissæ for the lower curve represent time in days, for the upper, time in hours. The influence of temperature is brought out very clearly. At 200° the velocity of esterification is 22,000 times as great as it is at 8°.7

1 M. Berthelot, Compt. Rend., 59. 616, 817, 861, 901, 1864; Ann Chim. Phys. [4], 18. 146, 1869.

2

J. Spohr, Zeit. phys. Chem., 2. 195, 1888.

3

4

J. Walker and J. K. Wood, Journ. Chem. Soc., 79. 21, 1900.

J. H. van't Hoff, Études, 112, 1884; T. Ewan's trans., 127, 1896.

5 V. Meyer and W. Raum, Ber., 28. 2804, 1895.

6 J. Dewar, Chem. News, 84. 281, 293, 1901.

7 M. Berthelot, Essai de Mécanique Chimique fondée sur la Thermo

chemie, Paris, 2. 93, 1879.